# How do you use the mean value theorem to explain why (-1) is the only zero of the function f(x)=x³+3x²+9x+7?

##### 1 Answer

Feb 23, 2017

Please see below.

#### Explanation:

If there were another zero, say at

then we could apply the mean value theorem on the interval

to conclude the=at there is a

But

Therefore, there cannot be two zeros of